Optimal weighting scheme for affected sib-pair analysis of sibship data

Application of the affected sib-pair method of linkage analysis to sibships with variable numbers of affected and unaffected members requires a scheme for weighting the contributions from the sibships in the calculation of an overall test statistic. Currently accepted weighting schemes are based on the concepts of independent pairs and Shannon information content. Here, we show that the weighting scheme with maximum power to detect linkage can be determined from the theoretical means and variances of the sibship contributions under the null and alternative hypotheses. We derive the theoretical means and variances of the contributions from different types of sibships under a generalized single locus model. We use these theoretical means and variances to obtain the optimal weights for a variety of single locus models, and compare the power of existing weighting schemes relative to the optimum. The results suggest that, under a range of plausible assumptions, optimal power is nearly obtained by weighting to all sibpairs equally, except those occurring in sibships with so many affected siblings (usually five or more) that the probability of parental homozygosity for the disease allele becomes substantial. A corollary is that, in affected sib-pair analysis, the 'informativeness' of a sibship is more nearly proportional to the number of affected sib-pairs than to the number of affected siblings, up to about five affected siblings.